{"id":2352,"date":"2024-11-23T20:00:09","date_gmt":"2024-11-23T12:00:09","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2352"},"modified":"2024-12-28T22:38:40","modified_gmt":"2024-12-28T14:38:40","slug":"jinyuan-chang-jing-he-lin-yang-yao-q-2023-modelling-matrix-time-series-via-a-tensor-cp-decomposition-journal-of-the-royal-statistical-society-series-b-85-127-148","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/en\/publications-en\/publications-all-en\/2352\/","title":{"rendered":"Chang, J., He, J., Yang, L., & Yao, Q. (2023). Modelling matrix time series via a tensor CP-decomposition. Journal of the Royal Statistical Society Series B: Statistical Methodology, 85, 127-148."},"content":{"rendered":"

We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method can significantly improve the finite-sample performance. We show that all the component coefficient vectors in the CP-decomposition can be estimated consistently. The proposed model and the estimation method are also illustrated with both simulated and real data, showing effective dimension-reduction in modelling and forecasting matrix time series.<\/p>\r\n\r\n